A 20 x 32 rectangle is embedded inside a 98 x 108 rectangle. They share a vertex and their sides partially over lap as shown. Find the distance between the centers of the two rectangles.

96 square yards would complete the room

Answer:

  (3±√147, 0) ≈ (-9.124, 0) and (15.124, 0)

Step-by-step explanation:

The points (x, 0) satisfy the distance formula:

  d = 14 = √((x -3)² +(0+7)²)

  196 = (x -3)² +49 . . . . . square both sides

  147 = (x -3)² . . . . . . . . . subtract 49

  3 ±√147 = x . . . . . . . . . take the square root and add 3

The points at distance 14 from (3, -7) on the x-axis are (3±√147, 0).

The GCF is 1.

Explanation:

1 has: 1 (LOL)

12 has: 1,2,3,4,6,12

16 has: 1,2,4,8,16

21 has: 1,3,7,21

24 has: 1, 2, 3, 4, 6, 8, 12, 24

30 has:  1, 2, 3, 5, 6, 10, 15, 30

44 has:  1, 2, 4, 11, 22, 44

70 has: 1, 2, 5, 7, 10, 14, 35, 70

So therefore, The GCF is 1

Hope this helps!

-Queenb369

P.S Could you possible give me the brainlist if i get it right.

The dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.

To solve this problem, we can use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:

vf² = vi² + 2ad

The positive value of d indicates that the dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.

The dolphin's friend is 5.3 meters below the surface of the water.

Let's reassess the problem with the given constraints more carefully.

We need to find the position of the dolphin's friend relative to the surface of the water.

1. Dolphin's height above the water:

[tex]\[ 4.5 \text{ meters above the surface} \][/tex]

2. Distance between the dolphin and her friend:

[tex]\[ 9.8 \text{ meters below the dolphin} \][/tex]

Since the friend is swimming below the dolphin, we need to subtract this distance from the height of the dolphin above the surface to find the position of the friend relative to the water surface.

3. Calculate the position of the dolphin's friend:

[tex]\[ \text{Position of friend} = 4.5 \text{ meters} - 9.8 \text{ meters} \][/tex]

[tex]\[ \text{Position of friend} = -5.3 \text{ meters} \][/tex]

This means the dolphin's friend is 5.3 meters below the surface of the water.

Answer: sin2y =240/289 where 0<y <π/2

Step-by-step explanation:

Given  sin(x) = 1/3 and sec(y) = 17/15 , where x and y lie between 0 and π/2.

We now that

[tex]cosy = \frac{1}{secy} =\frac{15}{17} \\and\\\text{using identity } sin^2y+cos^2y=1\\\text{we have}\\siny=\sqrt{1-cos^2y}=\sqrt{1-(\frac{15}{17} )^2}=\sqrt{1-\frac{225}{289} }=\sqrt{\frac{64}{289} }=\frac{8}{17} \\\Rightarrow\ siny=\frac{8}{17} \\\text{Now we are using identity sin2A=2sinAcosA we have}\\sin2y=2\cdot\ siny\cdot\ cosy=2\cdot\ \frac{8}{17} \cdot\ \frac{15}{17} =\frac{240}{289}[/tex]

To solve the question, we firstly find cos(y) from 'sec(y) = 17/15' because secant is the reciprocal of cosine. Then, we use the Pythagorean identity to find sin(y). Finally, we substitute these values into the double angle identity 'sin(2y) = 2sin(y)cos(y)' to find the final answer.

In this high school level mathematics problem, 'sin(x) = 1/3' and 'sec(y) = 17/15' are given. From 'sec(y) = 17/15', we can calculate cos(y) because secant is the reciprocal of cosine. Hence, 'cos(y) = 15/17'. The question asks for the evaluation of the expression 'sin(2y)'. Here, we can use a trigonometric identity for double angles, which states 'sin(2y) = 2sin(y)cos(y)'.

However, we are only given secant of y, not sine. To find sin(y), we can use the Pythagorean identity. According to this identity, 'sin^2(y) = 1 - cos^2(y)'. So, 'sin(y) = sqrt[1 - (15/17)^2]'.

So, the final answer becomes 'sin(2y) = 2 * √[1 - (15/17)²] * 15/17'. It's useful to note that you should always check that your angle lies within the given range when using a square root in trigonometry, to ensure your answer is correct.

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[tex]x^3-4^3 = (x-4)(x^2+4x+16)=(x-4)(x+4)(x+4)[/tex]

Remark

The diameter of the circle is AC. The hypotenuse of the right triangle is also AC. This assumes that A,B and C all lie on the circumference of the circle.

Answers

One

The center of the circle is on the diameter of the circle. In fact, the center bisects the diameter. So the center lies on AC and if the center is labeled O then AO = BO.

Answer 1: AC

Two

The answer is the single word diameter.

Answer:

Step-by-step explanation:

A vertical stretch by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x), where k <1.

If k =1, then same graph we obtain and if k>1 we get a vertically shrink graph.

In our question, there is a vertical stretch of 3. This means new graph would have points as (x,y/3)

i.e. instead of f(x) = y, we have now f(x) = y/3

So transformation is g(x) = 3f(x)

Option A is correct.

2) Here f(x) = 3x+8 is transformed to g(x) =3x+6

i.e. y intercept is reduced by 2 units.  Hence there is a translation of 2 units down.

I did not have the answer to the second question but here is the first.

Set up the proportion.  Then cross multiply and isolate the variable to solve.

[tex]\frac{8(trash bags)}{30 (days)} = \frac{x (trash bags)}{180 (days)}[/tex]

8(180)= 30(x)

[tex]\frac{8(180)}{30} = \frac{30x}{30}[/tex]

8(6) = x

48 = x

Answer: 48 trash bags

Answer:

The answer is Daniel is correct, but Kelly is not.

Step-by-step explanation:

Answer:

(D) Daniel is correct, but Kelly is not.

Step-by-step explanation:

It is given that Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles.

Kelly's Proof:∠2 = ∠4 (Vertical angles are congruent)

∠1 = ∠3 (Vertical angles are congruent)

Using Vertical Angle Theorem  the vertical angles are equal.

since, we cannot use the direct information given in the question in order to prove the same.

Thus, the justification given by Kelly is incorrect.

Now, Daniel's proof:

∠1 + ∠2 = 180°(Definition of Supplementary Angles)

and ∠1 + ∠4 = 180° (Definition of Supplementary Angles)

⇒∠1 + ∠2 = ∠1 + ∠4(Transitive Property of Equality)

Hence,  ∠2 = ∠4(Subtraction Property of Equality)

Thus, the justification of Daniel is correct.

Hence, option (D) is correct.

B

Assuming you mean the value of f(5)

If so then substitute x = 5 into f(x)

f(5) = (3 × 5) - 2 = 15 - 2 = 13 → B

We have been given the dimensions of the rectangular prism.

Lets say that the length, width, and height of the rectangular prism are:

Length [tex]= x+1[/tex]

Width [tex]=x-1[/tex]

Height[tex]=x[/tex]

Volume of a rectangular prism is given by:

[tex]length \times width\times height[/tex]

Plugging the values of length, width, and height, we get:

Total volume of the prism [tex]= (x+1)\times(x-1)\times x[/tex]

[tex]=(x^2-1)x=x^3-x[/tex]   (we have used [tex](a+b)\times (a-b)=a^2-b^2[/tex])

So, the expression for the total volume of the prism is:

[tex](x^3-x)[/tex]

Now for this you would have to think what two numbers multiplied to get 6x^2. Let's say for example 3x and 2x=6x^2

And now what two numbers multiplied together make -15, For example it can be 5 and -3

Now your ANSWER: (3x+5)(2x-3)

That would be choice C.

The graph of  4|x| is shaped like a V whose vertex is at the origin.

Every y value will be positive for y = 4|x|  as |x| is always positive  and a reflection in the x axis will make every y value negative.

Through moving up c units, the graphs of g can be determined from the graph of f. If we subtract c from f(x), the graph shifts downward. Let [tex]\bold{ h(x) = f(x) - c}[/tex]. Shifting downward c units yields this graph of h from the graph of f.

Given:

[tex]\bold{f(x)=4|x|}[/tex]

Calculation:

           [tex]\bold{g(x)=-(4|x|)}\\\\\bold{g(x)=-4|x|}\\\\[/tex]

So, the equation [tex]g(x)=-4|x|[/tex] describes [tex]g(x)[/tex].

Therefore, the final choice is "Option C".

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The unemployment rate is calculated as the number of unemployed divided by the labor force, resulting in approximately 9.6%, which is the closest to 9.3% as listed. It is higher than the historical average and the February 2015 rate.

The unemployment rate of an economy is calculated by taking the number of unemployed persons and dividing it by the total labor force, and then multiplying the result by 100 to get a percentage.

In this case, using the given figures, the unemployment rate is calculated as follows: 14.8 (unemployed) / 153.9 (labor force) = approximately 9.6%.

This indicates that the correct answer is not explicitly listed, but the closest answer given is 9.3%, which seems to be a typo.

Furthermore, this current unemployment rate is significantly higher than the February 2015 rate of 5.5% and above the historical average unemployment rate, which tends to range between 4% to 6% over time, according to Federal Reserve Economic Data.

Answer:

14. The correct option is 2.

13. The correct option is 4.

Step-by-step explanation:

14.

The given function is

[tex]f(x)=4|x|[/tex]

The function is non-negative for all values of x. So, the function opens in upward direction.

The function uis in the form of

[tex]f(x)=k|x|[/tex]

Where, a is vertical stretch factor or compress factor.

If k>1, then it represent vertical stretch and if 0<k<1, then it represent vertical compression.

Since the value of k is 4, therefore it represents vertical stretch and option 2 is correct.

13.

The given function is

[tex]y=x^3[/tex]

The traslate form of given function is

[tex]y=(x+a)^3+b[/tex]

Where, a represents the horizontal shift and b represents the vertical shift.

If a>0, then the graph shifts left side by a units and if a<0, then the graph shifts right side by a units.

If b>0, then the graph shifts upward by b units and if b<0, then the graph shifts downward by b units.

Since the graph shifts vertically 5 units down and horizontally 4 units left, therefore the value of a is 4 and value of b is -5. The required equation is

[tex]y=(x+4)^3-5[/tex]

Therefore option 4 is correct.

answer=3.20/16=0.20 is cost per ounce

Answer-

The total interest after 3 years is Rs.5760 .

Solution-

Total money borrowed = Rs.12000

Out of those Rs.4000 is of 18% interest rate and remaining 12000-4000=8000 is of 15% interest rate.

[tex]\text{Total interest}=\frac{P_1\times r_1\times t}{100}+\frac{P_2\times r_2\times t}{100}[/tex]

Where,

P₁ = principal amount = Rs.4000

P₂ = principal amount = Rs.8000

r₁ = rate of interest of P₁ = 18%

r₂ = rate of interest of P₂ = 15%

t = time period  = 3 years

[tex]\text{Total interest}=\frac{4000\times 18\times 3}{100}+\frac{8000\times 15\times 3}{100}=2160+3600=5760[/tex]

That would be FALSE

They have the same angles, so they're similar triangles.  For them to be congruent, the corresponding sides must have equal length.  Here we have two sides of length 7, but they're not corresponding sides.  If on the second triangle the 7 was the length of the side between the 60 and 62 degree vertices then we'd have equal corresponding sides and congruent triangles.

Answer: no

Step-by-step explanation: this answer would be FALSEEE

Perimeter = 2*14 + 2x   where x is length of the adjacent side

46 = 28 + 2x

2x =  18

x = 9 inches Answer

There would be 4 groups of 8 coins. 32/8=4 Hope I could help!!!

Answer:

Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]

Step-by-step explanation:

Given : A card is chosen from a standard deck of cards.

To find : What is the probability that the card is a queen, given that the card is a club?

Solution : It is the conditional probability

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

Let A is probability that card is queen.

Let B is the probability that card is a club.

Probability that card is queen given card is club [tex]P(A\cap B)=\frac{4}{52}=\frac{1}{13}[/tex]

Probability that card is club from deck of 52 cards [tex]P(B)=\frac{13}{52}=\frac{1}{4}[/tex]

To find probability that card is queen given that card is club [tex]P(A|B)[/tex]

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

[tex]P(A|B)=\frac{\frac{1}{13}}{\frac{1}{4}}[/tex]

[tex]P(A|B)=\frac{1\times4}{13\times 1}=\frac{4}{13}[/tex]

Therefore, Option A is correct.

Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]

Answer:

the correct answer was 1/13

Step-by-step explanation:

i took my test and put 4/13 which was wrong and said that 1/13 is the right answer

The answer is A=D apex

Answer:

It's the first one, I just literally got done taking the test it was my last question anyways.

The equation is y = 2x - 12

Equation in slope intercept form is

[tex]y = mx + b[/tex]

Where,

m = slope

b = y-intercept

Putting the value of slope in this equation:

[tex]y = 2x + b[/tex]

From this we can solve the equation for b

[tex]b = y - 2x[/tex]

[tex]b = -2 - 2(5)[/tex]

[tex]b = -12[/tex]

Now, the equation of y-intercept becomes

[tex]y = 2x - 12[/tex]